Finite Group Databasebeta

C22×Dic1052 #30682715

order16832
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic1052

Splittings

SylowC263 ⋊ C22×Q16

Subgroups

subgroupG/H
centerC23D1052
commutator, cosocleC4×C263C24
FrattiniC4C23×D263
FittingC22×C8×C263C2
socle, prime radicalC23×C263D4
hypercenterC22×C8D263
hypocenterC263C22×Q16
LCSG ▷ C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16832

Conjugacy classes & character table

4220 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#46783087, #46783089, #46783606, …
maximal normal subgroup of#46783087, #46783089, #46783606, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16832, 1326);